- the development of abstract reducibility candidates continues ...

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / substitution / lift_vector.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_vector.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_vector.ma
index ef422bdd4bc41eef2f93dc20184833c7099b8162..710ab34cd1db49a1f3cade0d7b1d4c5e6568e09a 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_vector.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_vector.ma
@@ -26,6 +26,31 @@ inductive liftv (d,e:nat) : relation (list term) ≝
 
 interpretation "relocation (vector)" 'RLift d e T1s T2s = (liftv d e T1s T2s).
 
+(* Basic inversion lemmas ***************************************************)
+
+fact liftv_inv_nil1_aux: ∀T1s,T2s,d,e. ⇧[d, e] T1s ≡ T2s → T1s = ◊ → T2s = ◊.
+#T1s #T2s #d #e * -T1s -T2s //
+#T1s #T2s #T1 #T2 #_ #_ #H destruct
+qed.
+
+lemma liftv_inv_nil1: ∀T2s,d,e. ⇧[d, e] ◊ ≡ T2s → T2s = ◊.
+/2 width=5/ qed-.
+
+fact liftv_inv_cons1_aux: ∀T1s,T2s,d,e. ⇧[d, e] T1s ≡ T2s →
+                          ∀U1,U1s. T1s = U1 :: U1s →
+                          ∃∃U2,U2s. ⇧[d, e] U1 ≡ U2 & ⇧[d, e] U1s ≡ U2s &
+                                    T2s = U2 :: U2s.
+#T1s #T2s #d #e * -T1s -T2s
+[ #U1 #U1s #H destruct
+| #T1s #T2s #T1 #T2 #HT12 #HT12s #U1 #U1s #H destruct /2 width=5/
+]
+qed.
+
+lemma liftv_inv_cons1: ∀U1,U1s,T2s,d,e. ⇧[d, e] U1 :: U1s ≡ T2s →
+                       ∃∃U2,U2s. ⇧[d, e] U1 ≡ U2 & ⇧[d, e] U1s ≡ U2s &
+                                 T2s = U2 :: U2s.
+/2 width=3/ qed-.
+
 (* Basic properties *********************************************************)
 
 lemma liftv_total: ∀d,e. ∀T1s:list term. ∃T2s. ⇧[d, e] T1s ≡ T2s.